While I will always defer to Meni with regards to the rigorous math, and I respect Luke-Jr's abilities and contributions to the bitcoin community, saying that any sort of credit system is not ultimately a downward spiral into oblivion over a long enough time frame is ludicrous.

You can take evidence, if from no other source, than trying to graph the luck of a pool, and it just happens to be a problem I've been working on lately. There is a lower bound to good luck, that being 1 share. There is no upper bound to bad luck - that is why, eventually, a pool issuing credit based on future work will eventually end up in the negative.

That said, it's entirely possible that in practice, that this eventuality would not happen in the expected pool lifetime, but to say that it will never happen is pure fallacy. The time frame for it happening is another issue entirely, and I would have no idea how to even try to calculate that.

The law of large numbers means that over time, any miner/pool's rewards will always drift toward average in the long run.

That said, it's entirely possible that in practice, that this eventuality would not happen in the expected pool lifetime, but to say that it will never happen is pure fallacy. The time frame for it happening is another issue entirely, and I would have no idea how to even try to calculate that.

Oh, we can calculate that, don't worry. You'll find (for pure Brownian motion) that the probability to reach a buffer of -m*B, starting from 0, at any time over a period of n rounds, is roughly 1-(m/sqrt(n))*sqrt(2/Pi). As n goes to infinity this goes to 1, so with probability 1 the buffer will reach that level eventually. However, it is interesting to note that the expected time to reach any level is infinite. Brownian motion is crazy.

dont know if anyone else is watching closelybutat ars= SMPPS Buffer -234.74753916 BTCdoesnt look good to me, been negative for over 24 hours and hashrate is dropping

It's not too bad if it stays negative as long as it's mild - it just means the maturity time will be about 5 blocks. But what some people may be missing is that there's no magic force pulling the balance towards 0 - that would be the gambler's fallacy. From -200 BTC it's as likely to go to -100 BTC as to -300 BTC.

The fact that pools get shut down due to lack of sufficient interest by the operator is another illustration of the problem with buffer methods. SMPPS is being marketed as "you will get 100% payout eventually". But if someone mines when the buffer is highly negative, and the pool gets shut down while he's waiting to receive payments, he will lose a significant portion of what he deserves. And this brings us back to the collapse scenario once the buffer becomes so low people realize it's better to go elsewhere.

The only thing open to interpretation here is whether using a method which is by design doomed to collapse is wrong. I say it is, but people are welcome to disagree on this.

While I will always defer to Meni with regards to the rigorous math, and I respect Luke-Jr's abilities and contributions to the bitcoin community, saying that any sort of credit system is not ultimately a downward spiral into oblivion over a long enough time frame is ludicrous.

You can take evidence, if from no other source, than trying to graph the luck of a pool, and it just happens to be a problem I've been working on lately. There is a lower bound to good luck, that being 1 share. There is no upper bound to bad luck - that is why, eventually, a pool issuing credit based on future work will eventually end up in the negative.

That said, it's entirely possible that in practice, that this eventuality would not happen in the expected pool lifetime, but to say that it will never happen is pure fallacy. The time frame for it happening is another issue entirely, and I would have no idea how to even try to calculate that.

The law of large numbers means that over time, any miner/pool's rewards will always drift toward average in the long run.

You beat me to posting. This is a fallacious interpretation of the law of large numbers known as the gambler's fallacy. The ratio between the pool's lifetime rewards and lifetime expected rewards will tend to 1, but their difference (which is the buffer) will not tend to 0 and will grow unboundedly in average magnitude. This can be easily verified by simulation.

While I will always defer to Meni with regards to the rigorous math, and I respect Luke-Jr's abilities and contributions to the bitcoin community, saying that any sort of credit system is not ultimately a downward spiral into oblivion over a long enough time frame is ludicrous.

You can take evidence, if from no other source, than trying to graph the luck of a pool, and it just happens to be a problem I've been working on lately. There is a lower bound to good luck, that being 1 share. There is no upper bound to bad luck - that is why, eventually, a pool issuing credit based on future work will eventually end up in the negative.

That said, it's entirely possible that in practice, that this eventuality would not happen in the expected pool lifetime, but to say that it will never happen is pure fallacy. The time frame for it happening is another issue entirely, and I would have no idea how to even try to calculate that.

The law of large numbers means that over time, any miner/pool's rewards will always drift toward average in the long run.

You beat me to posting. This is a fallacious interpretation of the law of large numbers known as the gambler's fallacy. The ratio between the pool's lifetime rewards and lifetime expected rewards will tend to 1, but their difference (which is the buffer) will not tend to 0 and will grow unboundedly in average magnitude.

No, gambler's fallacy is just assuming that the next block will move the buffer/credit toward 0. Over a long timeperiod, the law of large numbers does apply. The difference, while it might grow, will also have diminishing relevance, at least with ESMPPS. Real-world experiences show that the difference does not in practice grow unbounded, however.

While I will always defer to Meni with regards to the rigorous math, and I respect Luke-Jr's abilities and contributions to the bitcoin community, saying that any sort of credit system is not ultimately a downward spiral into oblivion over a long enough time frame is ludicrous.

You can take evidence, if from no other source, than trying to graph the luck of a pool, and it just happens to be a problem I've been working on lately. There is a lower bound to good luck, that being 1 share. There is no upper bound to bad luck - that is why, eventually, a pool issuing credit based on future work will eventually end up in the negative.

That said, it's entirely possible that in practice, that this eventuality would not happen in the expected pool lifetime, but to say that it will never happen is pure fallacy. The time frame for it happening is another issue entirely, and I would have no idea how to even try to calculate that.

The law of large numbers means that over time, any miner/pool's rewards will always drift toward average in the long run.

You beat me to posting. This is a fallacious interpretation of the law of large numbers known as the gambler's fallacy. The ratio between the pool's lifetime rewards and lifetime expected rewards will tend to 1, but their difference (which is the buffer) will not tend to 0 and will grow unboundedly in average magnitude.

No, gambler's fallacy is just assuming that the next block will move the buffer/credit toward 0. Over a long timeperiod, the law of large numbers does apply. The difference, while it might grow, will also have diminishing relevance, at least with ESMPPS. Real-world experiences show that the difference does not in practice grow unbounded, however.

ESMPPS is more complicated, but not very different from this regard, so I'll focus the discussion on SMPPS. The relevance of the difference does not diminish, because what determines the attractiveness of mining now (which is relevant for current miners considering quitting, and others considering joining) is the current difference, not the relative difference compared to the pool's lifetime earnings.

The mentioned "real-world experiences" are about as relevant as me tossing a coin and stating "real-world experience shows that coins land on tails". It's random. The statistical properties of the process are understood. Whatever you try to deduce from the experience has no bearing on what we expect from the process, it only means that your sample is too small. The expected magnitude of the difference does grow without bound as time passes, that's a fact. We can discuss the specifics of this growth if you'd like.

There is a lower bound to good luck, that being 1 share. There is no upper bound to bad luck - that is why, eventually, a pool issuing credit based on future work will eventually end up in the negative.

Actually, this has nothing to do with it. You'd have the same problems if both good and bad luck were bounded, or if bad luck was bounded and good luck was unbounded. Even a "reverse pool" which pays for found blocks and is paid for every share, will have the exact same long-term risk as a normal pool. The central limit theorem guarantees that whatever the payout distribution for a single round looks like (as long as its variance is finite), the process will over the long run be equivalent to Brownian motion.

Out of curiosity, how does LLN apply when we are talking about such low values in terms of the count of blocks. I would think that LLN would apply to many pools over a long period of time, but would not apply to a pool that doesn't have thousands and thousands of blocks over a long period of time. One or two thousand blocks doesn't seem like a sufficiently large number to apply?

The math is beyond me in either case, so that's why I ask.

*EDIT*

How can an unbounded good luck (and bounded bad luck) pool tend towards the negative? I suppose this may a be rhetorical question, though, since the math is likely fairly complicated?

If you're searching these lines for a point, you've probably missed it. There was never anything there in the first place.

Out of curiosity, how does LLN apply when we are talking about such low values in terms of the count of blocks. I would think that LLN would apply to many pools over a long period of time, but would not apply to a pool that doesn't have thousands and thousands of blocks over a long period of time. One or two thousand blocks doesn't seem like a sufficiently large number to apply?

The math is beyond me in either case, so that's why I ask.

The LLN per se doesn't really say anything meaningful about a finite number of blocks, but fortunately, the CLT does. Over a time period where the pool should find on average 1000 blocks, the distribution of number of blocks found is Poisson with mean 1000, which is to a very good approximation normal with mean 1000 and standard deviation 31.62. This means that with probability ~50%, the actual number of blocks will be between 979 and 1021. So for a PPLNS pool, the payout will be w.p. 50% between 97.9% to 102.1% of the average. For an SMPPS pool, the buffer will be w.p. 50% between -1050 to 1050 BTC, w.p. 25% above 1050 and w.p. 25% below -1050.

How can an unbounded good luck (and bounded bad luck) pool tend towards the negative? I suppose this may a be rhetorical question, though, since the math is likely fairly complicated?

It doesn't drift to negative in either case. The only thing affecting long-term behavior is the expectation and variance of the change per round. The bad luck is theoretically unbounded but highly negative values have rapidly diminishing probabilities so they don't have much effect on the overall distribution.

If the expectation is 0, the overall trend is to fluctuate according to Brownian motion, with a rate depending on the variance of the change per round. This means that any level - whether highly positive or highly negative - will be reached eventually. However, here Gambler's ruin comes into play - as long as it's positive you continue playing, but when it's sufficiently negative you quit, so you will eventually reach the point of ruin.

So would you say then that SMPPS is a form of gambling you're betting that the pool will swing positive or at worst to 0 while you mine?

You don't need it to get to >=0, as long as the balance stays mildly negative you'll get your payouts (in the limit). You're betting that the pool doesn't collapse (due to reaching a highly negative balance) before you finish getting your payouts.

So would you say then that SMPPS is a form of gambling you're betting that the pool will swing positive or at worst to 0 while you mine?

Its not such a big gamble . As long as you define a low enough Auto payout or manually do it every day.In the worse case you could lose a day ( maybe 2 ) of mining if the pools collapses before you get your payout.

Meni has been predicting the eventual fall of any 0% PPS SMPPS pool , Ars specifically, for a while now.I'm sure his math is correct- I guess it all goes to when "eventual" is.So far the hashers at ARS have gotten a premium service (most of the time ) and saved lots of BTC on fees.

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Its not such a big gamble . As long as you define a low enough Auto payout or manually do it every day.In the worse case you could lose a day ( maybe 2 ) of mining if the pools collapses before you get your payout.

There is no different here as far as SMPPS is involved. Raw PPS has an additional risk of "pool died, nobody got paid" because it promises more than it might be able to provide, but SMPPS never promises more than it has, so its balances are guaranteed to be available so long as someone doesn't steal it (eg, operator or some cracks the pool). Eligius intentionally doesn't keep a balance, by paying out as soon as you have accured a reasonable amount, so there is much less risk than other pools.